I just found that sometime even when the rank condition is not satisfied neither the Blanchard-Kahn condition, Dynare still does the simulation if I call simul. Then can I rely on the generated numbers? I think they are “arbitary” due to indeterminacy.
This is correct. Dynare can compute a deterministic simulation in case of local indeterminacy. It will use the initial numerical values in the first period of the simulation to choose one of the many trajectories, but there is no rational for this particular choice.